Research Interests
Combinatorics: latin squares (latin trades, defining sets), graph theory (graph decompositions).

Publications - 2012

Articles in Refereed Journals

Bryant, D., Cavenagh, Nicholas J., Maenhaut, Barbara, Pula, Kyle and Wanless, Ian M. (2012) Nonextendible Latin Cuboids SIAM J. on Discrete Maths Vol. 26, 239-249.

Donovan, Diane M., Lefevre, James G., McCourt, Thomas A., Cavenagh, Nicholas J. and Khodkar, Abdollah (2012) Identifying flaws in the security of critical sets in latin squares via triangulations Australian J. Combin. Vol. 52, 243–268.

Smith, Benjamin R. and Cavenagh, Nicholas (2012) Decomposing complete equipartite graphs into odd square-length cycles: Number of parts even Discrete Mathematics Vol. 312, 1611-1622.

Publications - 2011

Articles in Refereed Journals

Billington, Elizabeth J. and Cavenagh, Nicholas J. (2011) Decomposing complete tripartite graphs into 5-cycles when the partite sets have similar size Aequat. Math. 82, 277–289.

Billington, Elizabeth J., Cavenagh, Nicholas J. and Khodkar, Abdollah (2011) Super-simple twofold 4-cycle systems Bull. ICA Vol. 63, 48-50.

Cavenagh, Nicholas J. and Smith, B.R. (2011) Decomposing complete equipartite graphs into short even cycles J. Combin. Designs 19, 131-143.

Cavenagh, Nicholas J. and Stones, D. (2011) Near-automorphisms of latin squares J. Combin. Designs 19, 365-377.

Cavenagh, Nicholas J., Hamalaianen, C., Lefevre, J. and Stones, D. (2011) Multi-latin squares Discrete Math. 311, 1164-1171.

Publications - 2010

Articles in Refereed Journals

Billington, Elizabeth J., Cavenagh, Nicholas J. and Smith, Benjamin R. (2010) Path and cycle decompositions of complete equipartite graphs: 3 and 5 parts Discrete Math. 310, 241-254.

Cavenagh, Nicholas J. (2010) Avoidable partial latin squares of order 4m+1 Ars Combin. 95, 257—275.

Cavenagh, Nicholas J. and Smith, B.R. (2010) Decomposing complete equipartite graphs into short odd cycles Electronic J. Combin. 17, R130.

Cavenagh, Nicholas J. and Wanless, Ian M. (2010) On the number of transversals in Cayley tables of cyclic groups Discrete Appl. Math. 158, 136-146.

Publications - 2009

Articles in Refereed Journals

Billington, Elizabeth J., Cavenagh, Nicholas J. and Smith, Benjamin R. (2009) Path and cycle decompositions of complete equipartite graphs: Four parts Discrete Math. 309, 3061-3073.

Cavenagh, Nicholas J., Hamalainen, Carlo and Nelson, Adrian M. (2009) On completing three cyclically generated transversals to a latin square Science Direct (Finite Fields and Their Applications) 15, 294-303.